Question

A car moving with velocity 20m/s is brought to rest in 5s by applying brakes.
Calculate the acceleration of car? Can you identify that the car accelerated or retarded?

Answer 1

Explanation:

Given :

Initial velocity (u) = 20 m/s

Time taken (t) = 5 s

Final velocity (v) = 0 m/s

To find :

Acceleration or retardation ?

Solution :

Acceleration is given by,

⇒ Change in velocity/Time taken

That is,

⇒ (v - u)/t

Substituting we get,

⇒ (0 - 20)/5

⇒ -20/5

⇒ -4 m/s²

• The acceleration is -4 m/s², this indicates the body is retarding so the retardation is 4 m/s².

Answer 2

Given :

• Initial velocity of a car = 20 m/s

• Final velocity of a car = 0 m/s [It's final velocity is zero because the car comes to rest.]

• Time = 5 seconds

To find :

• The acceleration of the car

• To identify whether the car is accelerating or retardating

Concept :

Here, in this question we are given the initial velocity, final velocity and the time taken by the car to come to rest and we need to calculate the acceleration of the car. To calculate the acceleration we will use the first equation of motion.

First equation of motion :

• v = u + at

where,

• v denotes the final velocity
• u denotes the initial velocity
• a denotes the acceleration
• t denotes the time

Solution :

Calculating the acceleration of the car :

→ v = u + at

we have,

• v = 0 m/s
• u = 20 m/s
• t = 5 seconds

Substituting the given values :

→ 0 = 20 + (a)(5)

→ - 20 = a × 5

→ - 20/5 = a

→ - 4 = a

The acceleration of the car = - 4 m/s².

The value of acceleration is in negative. So, the car is retarding at 4 m/s².

Knowledge Bytes :

Second equation of motion :

• s = ut + ½ at²

Third equation of motion :

• v² - u² = 2as

where,

• s denotes the distance travelled
• v denotes the final velocity
• u denotes the initial velocity
• t denotes the time
• a denotes the acceleration